1. Field of the Invention
The present invention relates to a simulation apparatus, and corresponding method, for simulating the current flowing through elements of an electronic apparatus using the moment method and to a memory medium for storing programs for realizing the simulation apparatus and corresponding method and, more particularly, relates to a simulation apparatus and corresponding method using the moment method for executing simulation processing at a high speed and a memory medium for storing programs for realizing that the simulation apparatus and corresponding method.
Electronic apparatuses are also restricted by society from being affected by radio waves or noise radiated from other electronic apparatuses, which level is more than a certain level. Countries are also establishing tough regulations in this regard. To simulate quantitatively the radio waves generated by electronic apparatuses, it is necessary to calculate not only the radio waves generated by the printed circuit boards, but also the radio waves radiated due to the common mode current flowing through the cables and the shield effect of the housings etc.
Due to this, the present inventors have previously proposed a simulation technique using the moment method which calculates the current flowing through the elements of an electronic apparatus and uses that to calculate the radio waves radiating from the electronic apparatus. To make such a simulation technique practical, it is necessary to construct a configuration for realizing processing at a much higher speed (for example, see Japanese Unexamined Patent Publication (Kokai) No. 7-302278).
2. Description of the Related Art
The intensity of an electromagnetic field radiating from an object may be simulated by finding the electric current and the magnetic current flowing through parts of the object and then substituting the current into a known theoretical equation of the radiation of electromagnetic waves. The electric current and magnetic current flowing through the parts of the object theoretically can be obtained by solving Maxwell's electromagnetic wave equations under given boundary conditions.
One way to solve this is the moment method. The moment method is a method of solving integration equations derived from Maxwell's electromagnetic wave equations. It segments an object into small elements for which the electric current and magnetic current are then calculated. This makes it possible to handle any three-dimensionally shaped objects. A reference document on this moment method is "N. N. Wang, J. H. Richmond, and M. C. Gilreath: "Sinusoidal reaction formulation for radiation and scattering from conducting surface", IEEE Transactions Antennas Propagation, Vol. AP-23, 1975".
In the moment method, the configuration of the electronic apparatus to be simulated is segmented into elements. When the frequency to be processed is selected, the mutual impedance between segmented elements for that frequency is found by predetermined computation (when the mutual admittance and the mutual reaction are considered, found for these as well), the found mutual impedance and wave source specified by the configuration information are entered into the simultaneous equations of the moment method, and the equations are solved to find the electric current flowing through the elements (magnetic current as well when considering the mutual admittance and mutual reaction).
That is, the mutual impedance Z.sub.ij between segmented elements is found and the simultaneous equations of the moment method standing between the mutual impedance Z.sub.ij, the wave source V.sub.i, and the electric current I.sub.i flowing through the segmented elements EQU [Z.sub.ij ][I.sub.i ]=[V.sub.i ]
are solved to find the current Ii flowing through the segmented elements.
The related art regarding the derivation of the mutual impedance will be explained later in detail with reference to the drawings and equations.
The related art has the following advantages: That is, as clear from the equation of the mutual impedance between monopoles, "Z.sub.ij =Z.sub.ji " stands. From this, it is clear that the simultaneous equations of the moment method are symmetrical in form. Due to this, the number of the impedances to be calculated is reduced and the simultaneous equations can be calculated faster.
Further, the expansion function is a sinusoidal function and uses reaction matching (integration over an entire range on each monopole and, therefore, it becomes a double integration even in the case of a wire), so even if the number of the unknowns (number of segmented elements) is small, high precision calculation becomes possible. As opposed to this, if the expansion function is a pulse function and uses point matching (calculation of just one point for one monopole, therefore, the required integration becomes a single integration), a larger number of unknowns becomes necessary to achieve precision.
The time for solving simultaneous equations under the moment method is proportional to the cube of the unknowns, so if the expansion function is a sinusoidal function and reaction matching is adopted, a small number of unknowns is enough--which is very advantageous for analyzing large scale models.
The mutual impedances Z.sub.13, Z.sub.14, Z.sub.23, and Z.sub.24 between the above mentioned monopoles, however, cannot be calculated by elementary functions.
Due to this, in the related art, the method was adopted of expanding the mutual impedances between monopoles into a plurality of exponential integrals and calculating these exponential integrals by a numerical calculation scheme defined by formulas so as to calculate the mutual impedances between monopoles. Here, when the two monopoles are parallel (cos .phi.=1), there are eight exponential integrals expanded and when the two monopoles cross each other (cos .phi..noteq.1), there are 20.
Note that the numerical calculation scheme of the exponential integrals consists mainly of repetitive calculations, so time is taken even for calculation of one exponential integral. When the two monopoles are parallel, it takes eight times that time, while when the two monopoles cross (in this case, the range of integration becoming a complex number), it takes 20 times that time and therefore an extremely long time is required for the calculations.
Further, for the impedance between surface patches, a further long time is required for the calculation since the impedance is obtained by double integration of impedance between wires forming the surface patch.
Due to this, if, according to the related art, the moment method is used to simulate the electric current flowing through the elements of an electronic apparatus, there is the problem that an extremely long time is required for the processing.
Explaining the related art in more detail in accordance with the equation: ##EQU1## where, .intg..intg. denotes integrals from t.sub.0 to t.sub.1 and from z.sub.0 to z.sub.1
when the two monopoles are parallel (cos .phi.=1), by expanding this equation into eight exponential integrals, the following is obtained: ##EQU2## to a.sub.1n (real number). PA1 where, .intg. is the integral from .infin. to a specified value,
Further, when the two monopoles cross (cos .phi..apprxeq.1), by expanding the above equation of Z.sub.13 into 20 exponential integrals, the following is obtained: ##EQU3## where, .alpha..sub.n and .beta..sub.n are constants of complex numbers, the .SIGMA. of the first term is the sum for n=1 to 4,
the .SIGMA. of the second term is the sum for n=1 to 16, PA2 the .intg. of the first term is the integral from a.sub.0n (real number) to a.sub.1n (real number), and PA2 the .intg. of the second term is the integral from c.sub.0n (complex number) to c.sub.1n (complex number). PA2 .gamma. is Euler's constant, and PA2 .SIGMA. is the sum from n=1 to .infin..
Further, by substituting "jku" into "t", these exponential integrals ".intg.exp(-jku)/u.multidot.du" are modified to ##EQU4## where, .intg..sup.jkc1n is the integral from .infin. to jkc.sub.1n and .intg..sup.jkc0n is the integral from .infin. to jkc.sub.0n
Further, the terms are calculated repeatedly in accordance with the following formula until the necessary precision is obtained: EQU .intg.exp(-t)t.multidot.dt=.gamma.+log t+.SIGMA.[(-1).sup.n t.sup.n /(n!n)]
Normally, the calculation is repeated about n=10 to 20 times.
If following the related art in this way, there is the problem that an extremely long time is required for calculation of the mutual impedance between monopoles. Due to this, when using the moment method to simulate the electric current flowing through elements of an electronic apparatus, there is the problem that an extremely long time is required for the processing.